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If a and b are two positive real numbers such that 4a2 + b2 = 20 and ab = 4, then the value of 2a + b is:
1. 80
2. 8
3. 6
4. 5

1 Answer

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Best answer
Correct Answer - Option 3 : 6

Given :

4a2 + b2 = 20

ab = 4

To find :

2a + b

Formula used :

a2 + b2 = (a + b)2 - 2ab

Solution :

4a2 + b2 = 20

⇒ (2a)2 + b2 = 20

⇒ (2a + b)2 - 2 × 2a × b = 20

⇒ (2a + b)2 - 4 × 4 = 20

⇒ (2a + b)2 - 16 = 20

⇒ (2a + b)2 = 20 + 16

⇒ (2a + b)2 = 36

⇒ 2a + b = √36

⇒ 2a + b = 6

∴ the value of 2a + b is 6.

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